Physical probability in the Everett interpretation and Bell inequalities

TL;DR

This paper introduces a notion of locality compatible with the Everett interpretation, deriving the Born rule and explaining Bell inequality violations without action at a distance, supporting the many-worlds view.

Contribution

It develops a theory of physical probability for the Everett interpretation that satisfies a modified locality principle and accounts for Bell inequality violations.

Findings

Bell inequalities are derived with two loopholes.

The Born rule is derived within the Everett interpretation.

Bell inequality violations support the many-worlds interpretation.

Abstract

I define a notion of locality LOC, closely modelled on the Bell principle of Local Causality, construed as the condition that single case probabilities cannot be modified by actions at spacelike separation. The new principle, like that of Bell, forces Bell inequalities, but with two loopholes: one is violation of measurement independence, known to Bell, but the other is non-uniqueness of remote outcomes, a loophole only for LOC, not for Local Causality. I also set out a theory of physical probability, applicable to the Everett interpretation, in which the Born rule is derived, and which therefore violates Bell inequalities. I show it is consistent with LOC. Surprisingly, both loopholes are exploited. I conclude not only that physical probability in the Everett interpretation involves no action at a distance, but that the observed violation of Bell inequalities is powerful evidence for many worlds.